Changes

As shown in Wu et. al, the null distribution of the <math> \mathbf{Q} </math> statistic follows a mixture chi-sqaured distribution described as

As shown in Wu et. al, the null distribution of the <math> \mathbf{Q} </math> statistic follows a mixture chi-sqaured distribution described as

<math>\mathbf{Q}\sim\sum_{i=1}^m{\lambda_i\chi_{1,i}^2}, </math> where <math>\left(\lambda_1,\lambda_2,\dots,\lambda_m\right)</math> are eigen values of <math>\left(\sum_{i=1}^n{\mathbf{V_i}}\right)^\frac{1}{2}\mathbf{W}\left(\sum_{i=1}^n{\mathbf{V_i}}\right)^\frac{1}{2}</math>

<math>\mathbf{Q}\sim\sum_{i=1}^m{\lambda_i\chi_{1,i}^2}, </math> where <math>\left(\lambda_1,\lambda_2,\dots,\lambda_m\right)</math> are eigen values of <math>\mathbf{V_{meta}^\frac{1}{2}}\mathbf{W}\mathbf{V_{meta}^\frac{1}{2}}</math>